A sensitivity-enhanced fiber-optic refractive index (RI) sensor based on a tapered single-mode thin-core diameter fiber is proposed and experimentally demonstrated. The sensor head is formed by splicing a section of tapered thin-core diameter fiber (TCF) between two sections of single-mode fibers (SMFs). The cladding modes are excited at the first SMF-TCF interface, and then interfere with the core mode at the second interface, thus forming an inter-modal interferometer (IMI). An abrupt taper (tens of micrometers long) made by the electric-arc-heating method is utilized, and plays an important role in improving sensing sensitivity. The whole manufacture process only involves fiber splicing and tapering, and all the fabrication process can be achieved by a commercial fiber fusion splicer. Using glycerol and water mixture solution as an example, the experimental results show that the refractive index sensitivity is measured to be 0.591 nm for 1% change of surrounding RI. The proposed sensor structure features simple structure, low cost, easy fabrication, and high sensitivity.